We have Lake Shawnee on the East side of town, not too far off of HWY 70. Aside from that and local historical landmarks, Capitol, Brown vs Board, etc..., I can't recommend any hot spots. I just don't know of any. Lawrence, Kansas is just 20 minutes East and is full of great food and drink.

Here is what I recommend for food in Topeka.

Blind Tiger Brewery and Restaurant (I do love, love, love many of their beers but their food is consistently missing the mark, IMHO. But the beer... Man, go here.)

RowHouse Restaurant (Pricey, great food, only open for dinner Wednesday through Saturday.)

A.J.'s Pizzeria (You guessed it, pizza. This place has never left me disappointed. Tallgrass Brewery cans available, can't remember any other breweries served.)

The Burger Stand (A great gourmet hamburger joint with a full bar. Also has Blind Tiger and Free State Brewery on draft. My favorite place in town.)

Blind Tiger Brewery and Restaurant (I do love, love, love many of their beers but their food is consistently missing the mark, IMHO. But the beer... Man, go here.)

I always liked their food, but it's been a long time since I've been there.

As for what to do, like others said it's dependent on when you go. Topeka is fairly close to Lawrence, Manhattan, and KC. The BBQ festival in KC is always worth the side trip if you're in the area that time of the year. There's usually something going on at the convention center. In the summer you can catch NASCAR, NHRA, or ALMS races at the track. There's the air museum at the ANG base and they used to host an air show once every summer.

A few places you need to go. Lawrence it's full of great places to check out and eat at. Dempseys pub is home to some of the best burgers I have eaten and was a staple while I was in school at KU. Crown Center is close to downtown Kansas city and has lots to do and see depending on the time of year. The Plaza "is" downtown Kansas City and has lots of shopping, restaurants, and lots of really cool architecture and fountains. The best BBQ in Kansas City is the original Arthur Bryant's in the jazz district. KC power and Light district is really cool too.